Bipolar transistor frequency doublers at millimeter-wave frequencies

ABSTRACT

Frequency multipliers include a pair of transistors each connected to a common impedance through a respective collector impedance formed from a transmission line. Each transmission line has a length between about one quarter and about one eighth of a wavelength of an input signal frequency and is tuned to produce a large impedance at a collector of the respective transistor at the input signal frequency. The output frequency between the collector impedances and the common impedance is an even integer multiple of the input frequency.

RELATED APPLICATION DATA

This application is a Continuation application of co-pending U.S. patentapplication Ser. No. 13/747,915 filed on Jan. 23, 2013, incorporatedherein by reference in its entirety.

BACKGROUND

1. Technical Field

The present invention relates to frequency multipliers and, inparticular, to frequency multipliers operating at millimeter wavefrequencies.

2. Description of the Related Art

Frequency doublers and frequency multipliers in general are componentsof millimeter wave (mmWave) data communication, radar and imagingsystems. In any semiconductor technology, direct signal generationthrough an oscillator becomes more difficult as the fundamentalfrequency increases. High frequency oscillators tend to have lowertuning range, higher phase noise, higher power consumption and decreasedrobustness against temperature and other environmental variations thanoscillators generating low frequencies. For these reasons, to generate agiven frequency in the mmWave regime, a common alternative is to employa robust oscillator at a moderate frequency followed by a frequencymultiplier.

Conventional frequency doublers use two transistors driven with adifferential signal at a fundamental frequency w and a common loadZ_(L). The current at the second harmonic, having a frequency of 2w, hastwo components. The first is the second harmonic of the currentgenerated by each transistor. While the current generated at thefundamental frequency has an opposite phase for each transistor andcancels out, the current at the second harmonic has the same phase fromeach transistor, and hence adds coherently. To enhance this component,transistors are usually biased below their threshold voltage, wheretheir response is non-linear. This enhances harmonic generation butreduces operation speed and saturated output power. The second componentcomes from the fact that the output voltage swings twice for every cycleof the differential input signal. However, in a conventional frequencydoubler, the output impedance at the fundamental frequency is a short,which makes the voltage swing at collector nodes small. This small swingat the collector prevents transistors from generating high power at highefficiency.

Conventional frequency doublers therefore rely on the constructiveaddition of the two above-described components. However, thisconstructive addition only occurs for a limited range of input powers.Furthermore, the range and the associated conversion gain are vulnerableto device and temperature variations, which affect the threshold voltageand hence the device's non-linearity.

SUMMARY

A frequency multiplier is shown that includes a pair of transistors eachconnected to a common impedance through a respective collector impedanceformed from a transmission line, said transmission line having a lengthbetween about one quarter and about one eighth of a wavelength of aninput signal frequency and being tuned to produce a large impedance at acollector of the respective transistor at the input signal frequency,wherein an output frequency between the collector impedances and thecommon impedance is an even integer multiple of an input frequency.

A frequency multiplier is shown that includes a pair of transistors eachconnected to a common impedance through a respective collector impedanceformed from a transmission line, said transmission line having a lengthbetween about one quarter and about one eighth of a wavelength of aninput signal frequency and being tuned to produce a large impedance at acollector of the respective transistor at the input signal frequency,wherein an output frequency between the collector impedances and thecommon impedance is an even integer multiple of an input frequency; apair of reflecting transmission lines having a length that correspondsto about one quarter wavelength of a harmonic corresponding to theoutput signal and having an open end; and a pair of phase shiftingtransmission lines, each connecting a base terminal of a transistor to arespective one of the pair of reflecting transmission lines, having alength that phase shifts a reflected signal from the reflectingtransmission lines to add constructively with harmonic components of theinput signal.

A frequency multiplier is shown that includes a pair of differentiallydriven transistors each connected to a common impedance through arespective collector impedance formed from a transmission line, saidtransmission line having a length of about one quarter a wavelength ofan input signal frequency and being tuned to produce a large impedanceat a collector of the respective transistor at the input signalfrequency, wherein an output frequency between the collector impedancesand the common impedance is double the input frequency; a pair ofreflecting transmission lines having a length that corresponds to aboutone quarter wavelength of a frequency-doubled input signal and having anopen end; a pair of phase shifting transmission lines, each connecting abase terminal of a transistor to a respective one of the pair ofreflecting transmission lines, having a length that phase shifts areflected signal from the reflecting transmission lines to addconstructively with harmonic components of the input signal; and a pairof neutralization capacitors, each connecting the base terminal of atransistor to an opposite collector transmission line to compensate forfeedback capacitance in the transistors.

A receiver is shown that includes one or more radio frequency front endsconfigured to receive an input signal; and a frequency multiplierconfigured to increase the frequency of the input signal by an eveninteger multiple. The frequency multiplier includes a pair oftransistors each connected to a common impedance through a respectivecollector impedance formed from a transmission line, said transmissionline having a length between about one quarter and about one eighth of awavelength of an input signal frequency and being tuned to produce alarge impedance at a collector of the respective transistor at the inputsignal frequency, wherein an output frequency between the collectorimpedances and the common impedance is an even integer multiple of aninput frequency; a pair of reflecting transmission lines having a lengththat corresponds to about one quarter wavelength of afrequency-multiplied input signal and having an open end; a pair ofphase shifting transmission lines, each connecting a base terminal of atransistor to a respective one of the pair of reflecting transmissionlines, having a length that phase shifts a reflected signal from thereflecting transmission lines to add constructively with harmoniccomponents of the input signal; and a pair of neutralization capacitors,each connecting the base terminal of a transistor to an oppositecollector transmission line to compensate for feedback capacitance inthe transistors.

A method for frequency multiplying is shown that includes receiving asignal having an input frequency at a frequency multiplier comprising apair of transistors; and selecting a harmonic in the signal byconnecting the transistors to a common impedance through a respectivecollector impedance, wherein an output frequency at the harmonic betweenthe collector impedances and the common impedance is an even integermultiple of an input frequency.

A method for frequency multiplying is shown that includes receiving asignal having an input frequency at a frequency multiplier comprising apair of transistors; selecting a harmonic in the signal by connectingthe transistors to a common impedance through a respective collectorimpedance, wherein an output frequency at the second harmonic betweenthe collector impedances and the common impedance is an even integermultiple of an input frequency; reflecting harmonic feedback in theinput signal from the transistors using a pair of reflectingtransmission lines having a length that corresponds to about one quarterwavelength of a frequency-doubled input signal and having an open end;and phase shifting the reflected harmonic feedback using a pair of phaseshifting transmission lines, each connecting a base terminal of atransistor to a respective one of the pair of reflecting transmissionlines, having a length that phase shifts a reflected signal from thereflecting transmission lines to add constructively with harmoniccomponents of the input signal.

A method for frequency doubling is shown that includes receiving asignal having an input frequency at a frequency doubler comprising apair of transistors, where the signal is provided to the pair oftransistors differentially such that a fundamental component of thesignal cancels out; selecting a second harmonic in the signal byconnecting the transistors to a common impedance through a respectivecollector impedance, wherein an output frequency at the second harmonicbetween the collector impedances and the common impedance is double theinput frequency; reflecting second harmonic feedback in the input signalfrom the transistors using a pair of reflecting transmission lineshaving a length that corresponds to about one quarter wavelength of afrequency-doubled input signal and having an open end; phase shiftingthe reflected second harmonic feedback using a pair of phase shiftingtransmission lines, each connecting a base terminal of a transistor to arespective one of the pair of reflecting transmission lines, having alength that phase shifts a reflected signal from the reflectingtransmission lines to add constructively with harmonic components of theinput signal; and neutralizing parasitic capacitance using a pair ofneutralization capacitors, each connecting the base terminal of atransistor to an opposite collector transmission line to compensate forfeedback capacitance in the transistors.

These and other features and advantages will become apparent from thefollowing detailed description of illustrative embodiments thereof,which is to be read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure will provide details in the following description ofpreferred embodiments with reference to the following figures wherein:

FIG. 1 is a diagram of a frequency multiplier according to the presentprinciples;

FIG. 2 is a diagram of a frequency multiplier with feedback reflectionaccording to the present principles;

FIG. 3 is a diagram of a frequency multiplier with capacitanceneutralization according to the present principles;

FIG. 4 is a diagram of a receiver with a frequency multiplier accordingto the present principles;

FIG. 5(a) is a graph showing current in a frequency multiplier withoutcollector impedances;

FIG. 5(b) is a graph showing current in a frequency multiplier accordingto the present principles;

FIG. 6 is a graph comparing the power added efficiency of embodimentswith and without collector impedances;

FIG. 7(a) is a graph of temperature response of a frequency doubleraccording to the present principles;

FIG. 7(b) is a graph of temperature response of a conventional frequencydoubler;

FIG. 8 is a graph comparing the output power of frequency multipliersaccording to the present principles with and without neutralizationcapacitors;

FIG. 9 is a graph comparing power consumption of frequency multipliersaccording to the present principles with and without neutralizationcapacitors;

FIG. 10 is a graph showing a simulation of a frequency multiplieraccording to the present principles that exemplifies harmonic responseaccording to resonator length;

FIG. 11 is a diagram of a frequency quadrupler according to the presentprinciples; and

FIG. 12 is a block/flow diagram of a frequency multiplying methodaccording to the present principles.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The present principles provide frequency doublers which have highergain, saturation power, and efficiency compared to conventionalfrequency doublers. The embodiments disclosed herein furthermore aremore robust to temperature changes, as current shaping is provided bycollector voltage swing rather than from base voltage clippingdetermined by DC bias and the threshold voltage. To achieve theseeffects, the present principles employ current shaping with collectorload, optimum harmonic termination at the input, and input capacitanceneutralization.

Referring now to the drawings in which like numerals represent the sameor similar elements and initially to FIG. 1, a frequency doubler isshown according to the present principles. A common load Z_(L) 102 isshown, with an output voltage at 103 having a doubled frequency of 2w.Two input terminals are present, having a positive voltage input 112 anda negative voltage input 110, each having a fundamental frequency of w.Impedances Z_(c) 104 at the collectors of transistors 106 are formedusing, e.g., a transmission line having a length of approximately onequarter the wavelength of the input frequency w, giving a high collectorimpedance at the fundamental frequency. In this way, the collectorimpedances 104 modulate the collector current by having a large voltageswing at the collector. A bias voltage 116 is applied to the base of thetransistors 106 through resistors 114 to bias the transistors 106 at theoptimum point to maximize harmonic generation. The resistance value ofresistors 114 should be much larger than the input impedance oftransistors 106, so as not to affect AC operation.

This produces two results: First, the second harmonic content of thecollector current will be larger at relatively high input amplitudesand, second, the overall power dissipated at the device—the product ofthe collector current and the collector voltage—will be lower becauseboth voltage and current exhibit a switching behavior and do not overlapin time domain. Because in this mode of operation the second harmonicgeneration depends on the collector current shaping rather than ontransconductance non-linearity, the V_(B) terminal 116 can be higherthan the threshold voltage of the transistors 106; this increases thegain of the device at high frequencies thus providing higher frequencydoubler conversion gain and efficiency. For the second harmonic at 2w,the exemplary transmission line collector impedances 104 have about halfthe wavelength and are therefore transparent. In other words, the secondharmonic current directly sees the impedance Z_(L).

Described in general terms, the present principles provide a relativelylarge impedance 104 at the collector of each transistor 106 instead of adirect short. This creates a significant collector voltage waveformwhich has the fundamental frequency as its main component, but has otherharmonics as well. Because the two transistors 106 are drivendifferentially, the fundamental component is always cancelled, whereasthe harmonics may prevail. The large signal swing at the collectorboosts efficiency because, for significant periods of time, the voltagedrop across transistors 106 will be low. The large impedance 104 may beimplemented, as described above, as a transmission line. As the lengthof the transmission line decreases, the overall collector voltage swingreduces as well, but the shape and overall phase difference betweencurrent and voltage may be such that other harmonics (2^(nd), 4^(th),6^(th), etc.), are generated efficiently.

It is to be understood that the present invention will be described interms of a given illustrative architecture having a substrate orflexible substrate; however, other architectures, structures, substratematerials and process features and steps may be varied within the scopeof the present invention.

It will also be understood that when an element such as a layer, regionor substrate is referred to as being “on” or “over” another element, itcan be directly on the other element or intervening elements may also bepresent. In contrast, when an element is referred to as being “directlyon” or “directly over” another element, there are no interveningelements present. It will also be understood that when an element isreferred to as being “connected” or “coupled” to another element, it canbe directly connected or coupled to the other element or interveningelements may be present. In contrast, when an element is referred to asbeing “directly connected” or “directly coupled” to another element,there are no intervening elements present.

Embodiments in accordance with the present principles may include adesign for an integrated circuit chip, which may be created in agraphical computer programming language, and stored in a computerstorage medium (such as a disk, tape, physical hard drive, or virtualhard drive such as in a storage access network). If the designer doesnot fabricate chips or the photolithographic masks used to fabricatechips, the designer may transmit the resulting design by physical means(e.g., by providing a copy of the storage medium storing the design) orelectronically (e.g., through the Internet) to such entities, directlyor indirectly. The stored design is then converted into the appropriateformat (e.g., GDSII) for the fabrication of photolithographic masks,which typically include multiple copies of the chip design in questionthat are to be formed on a wafer. The photolithographic masks areutilized to define areas of the wafer (and/or the layers thereon) to beetched or otherwise processed.

Methods as described herein may be used in the fabrication of integratedcircuit chips. The resulting integrated circuit chips can be distributedby the fabricator in raw form (that is, as a single flexible substratethat has multiple structures formed thereon), as a bare die, or in apackaged form. In the latter case the chip is mounted in a single chippackage (such as a plastic carrier, with leads that are affixed to amotherboard or other higher level carrier) or in a multichip package(such as a ceramic carrier that has either or both surfaceinterconnections or buried interconnections). In any case the chip isthen integrated with other chips, discrete circuit elements, and/orother signal processing devices as part of either (a) an intermediateproduct, such as a motherboard, or (b) an end product. The end productcan be any product that includes integrated circuit chips, ranging fromtoys and other low-end applications to advanced computer products havinga display, a keyboard or other input device, and a central processor.

Referring now to FIG. 2, harmonic termination is shown at the inputs oftransistors 106. Due to parasitic capacitances between collector andbase, there may be signal feedback at the second harmonic between theoutput and the input of the transistors 106. This can be addressed byadding impedances 202 and 204 that represent a “short” at the secondharmonic after a certain amount of phase shift through 202. Impedance204 may be implemented using, e.g., a transmission line having a lengththat corresponds to one quarter of the wavelength at 2w and has an openend, thus behaving as a short. This reflects any signal at 2w that comesinto impedance 204. The present embodiment also provides a secondimpedance 202, which may be implemented using a transmission linebetween the input to the transistor 106 and the short 204. The optimallength of 202 can be determined so that a reflected 2w signal fromimpedance 204 can experience a desired amount of phase shift forconstructive interference with the existing second harmonic componentsbefore the signal reaches the base of transistor 106. Impedances 202 and204 provide feedback in the second harmonic in such a way that it addsconstructively with the harmonic content generated by the rest of thestructure. This is in contrast to conventional frequency doublers, whichwould try to prevent current feedback from the collector-base capacitorfrom being converted into voltage at the base. In other words, whereas aconventional frequency doubler attempts to cancel feedback, the presentinvention uses such feedback constructively.

Referring now to FIG. 3, input capacitance neutralization is shown. Dueto a high gain at the fundamental frequency w, a parasitic capacitancedue to the Miller effect dominates the total input capacitance. TheMiller effect depends on the input power, because at some point the gainat the fundamental frequency w compresses. Therefore, different inputmatching is used to obtain efficient operation at different powerlevels. In the present embodiment, neutralization capacitors 302 areconnected between the input of each transistor 106 and connected to thecollector of the other transistor 106. The neutralization capacitors 302compensate for the feedback capacitance of transistors 106. As a result,the circuit exhibits a relatively constant input capacitance atdifferent power levels. This is particularly beneficial at relativelylow input powers, where higher conversion gains can be obtained usinginput capacitance neutralization.

Referring now to FIG. 4, an exemplary mmWave receiver is shown thatillustrates how a frequency doubler may be used. The receiver 400 hasmultiple antennas 401, each leading to a respective radio frequencyfront end 402 that performs initial reception and processing. The poweroutputs of each front end 402 are combined in a power combiner 404,which sends its output to receiver core 406. The receiver core 406performs additional processing, but first down-converts the input signalto an intermediate frequency (IF). To accomplish this, a frequencymultiplier 408 generates a signal according to the present principlesthat is mixed with the input signal at mixer 410, producing a multipliedsignal.

A frequency doubler can also be employed in a phased-array transmitter.In this case, the doubler drives an up-conversion mixer which convertsthe signal to be transmitted from IF to RF. Subsequently the RF isdistributed to multiple RF front-ends.

Referring now to FIG. 5, graphs are shown that compare embodiments with(a) and without (b) the collector impedances 104. In each graph, a solidline shows the current at the collector of transistors 106, measured inmilliamps, while a dotted line shows the voltage at the collector,measured in volts. FIG. 5(a) clearly shows a much more pronounced secondharmonic that causes the depicted two-hump structure of the waveform. Incontrast, the 5(b) graph has a much smoother curve that lacks pronouncedsecond harmonic effects. Furthermore, the collector impedances 104 causea substantially increased voltage swing at the collector in graph 5(a)as compared to graph 5(b). The high voltage swing allows the use ofpower-efficient operation.

Referring now to FIG. 6, the power added efficiency (PAE) of the presentembodiments with collector impedances 104 and without neutralizationcapacitors 302 are shown in comparison to conventional frequencydoublers. The PAE is measured against the input power. The input poweris measured in decibels with a reference of one milliwatt (dBm) and PAEis measured in percentage (%) as a ratio of output power at 2w to totalinput power including supplied DC and AC at w. A dotted line representsthe PAE of conventional frequency doublers, while the solid linerepresents the PAE of the present embodiments. As is evident from thegraph, the present embodiments provide much higher efficiencies athigher powers. Moreover, in the present embodiment, lower efficiency atlow input power can be improved by using neutralization capacitors 302as shown in FIG. 8 and as described below.

Referring now to FIG. 7, the temperature response of the presentembodiments (a) is compared to the temperature response of conventionalfrequency doublers (b). In each case, the output power is measured indecibels and compared to input power, measured in decibels. A dottedline shows the power response as measured at 27 degrees Celsius, while adotted line shows the same device measured at 85 degrees Celsius, bothat a fundamental frequency of w=42 GHz. The two curves track closely inthe present embodiment, showing robustness against significant changesin temperature, while conventional frequency doublers show substantialdivergence under the same temperatures.

Referring now to FIG. 8, a comparison between the present embodimentswith neutralization capacitors 302 and the embodiments withoutneutralization capacitors 302. The output power is measured in decibelsand shown against input power, also measured in decibels. A solid lineshows the results of a device using a neutralization capacitor 302having a capacitance of 10 fF, while the dashed line shows the responseof the present embodiments without neutralization. The graph shows thatneutralization capacitors 302 provide better input matching for a broadrange of input powers by cancelling out the parasitic feedbackcapacitance.

Referring now to FIG. 9, a comparison of DC power consumption is shown.DC power consumption is measured in milliwatts against input power,measured in decibels. A solid line shows the power consumption of anembodiment having neutralization capacitors 302, while a dashed lineshows power consumption for the present embodiment withoutneutralization capacitors 302. As can be seen from the graph, the powerconsumption of a neutralized frequency doubler is substantially lowerthan that of conventional designs.

It should be recognized that the present principles may be extended toembodiments providing greater frequency multipliers. Even frequencymultipliers greater than two can be implemented by adjusting a collectorimpedance to have a different phase relation between voltage and currentat the output. A different phase shift changes the portion of harmonicsby having a different current waveform in time domain. For example, anarrower current waveform has higher power at higher harmonics.Capacitance neutralization can be employed for any differential type ofeven-numbered frequency multipliers to improve conversion gain at lowinput power. The present principles do not provide for odd-numberedmultipliers, because any even harmonic adds constructively at the commonimpedance 102 and all odd harmonics cancel.

Referring now to FIG. 10, a simulation is shown that displays outputpower from different even harmonics as a function of the length of atransmission line 104 at the collector of transistors 106. The secondharmonic is shown as a solid line, with the fourth harmonic shown usinghollow dots and the sixth harmonic shown using solid dots. The length ofthe transmission line 104 is shown in micrometers on the x-axis, withoutput power being shown on the y-axis. Transmission lines 104 havingdifferent loads produce different phase shifts between the collectorvoltage and current, resulting in different collector current waveformsin the time domain. For example, 550 μm is an optimal transmission linelength to maximize the fourth harmonic to operate as a frequencyquadrupler. Similarly, 720 μm is optimal for a frequency doubler,because the second harmonic is at a maximum.

In the simulation shown in FIG. 10, only the length of the collectortransmission line 104 is varied, with everything else being heldconstant. When the transmission line is 550 μm, the 4^(th) harmonicincreases but is still smaller than the second. To operate the circuitas a frequency quadrupler, where the 4^(th) harmonic is the largesttone, other modifications may be introduced.

Referring now to FIG. 11, a frequency quadrupler is shown. A reflectingtransmission line having a length that corresponds to about one quarterwavelength of a frequency-doubled input signal and having an open end isplaced at the junction between the common impedance 102 and thecollector impedances 104. The transmission line 1102 acts as a stubfilter, removing the second harmonic. Because the total power generatedby the multiplier should remain approximately constant, due to theconservation of energy, suppressing the second harmonic in turn enhancesthe energy of the fourth. The common impedance 102 in this case can bethe final load impedance of the multiplier, such as an on-chip antenna.

Referring now to FIG. 12, a method for multiplying an input frequency isshown. Block 1202 selects a second harmonic from transistors 106 using,e.g., transmission lines 104 as described above. These transmissionlines 104 have a length that selectively emphasizes the second harmonicof the signal, producing a frequency-doubled signal. Block 1204 uses areflecting transmission line 204 before the transistors 106 to reflectback any feedback in the second harmonic. Block 1206 phase shifts thereflected second harmonic using an appropriate transmission line 202before block 1206 constructively adds the reflected second harmonic withthe input signal. Block 1208 neutralizes the parasitic capacitance attransistors 106 by implementing neutralizing capacitors between thetransistors 106.

Reference in the specification to “embodiments,” “one embodiment,” or“an embodiment” of the present principles, as well as other variationsthereof, means that a particular feature, structure, characteristic, andso forth described in connection with the embodiment is included in atleast one embodiment of the present principles. Thus, the appearances ofthe phrase “in one embodiment” or “in an embodiment”, as well any othervariations, appearing in various places throughout the specification arenot necessarily all referring to the same embodiment.

It is to be appreciated that the use of any of the following “/”,“and/or”, and “at least one of”, for example, in the cases of “A/B”, “Aand/or B” and “at least one of A and B”, is intended to encompass theselection of the first listed option (A) only, or the selection of thesecond listed option (B) only, or the selection of both options (A andB). As a further example, in the cases of “A, B, and/or C” and “at leastone of A, B, and C”, such phrasing is intended to encompass theselection of the first listed option (A) only, or the selection of thesecond listed option (B) only, or the selection of the third listedoption (C) only, or the selection of the first and the second listedoptions (A and B) only, or the selection of the first and third listedoptions (A and C) only, or the selection of the second and third listedoptions (B and C) only, or the selection of all three options (A and Band C). This may be extended, as readily apparent by one of ordinaryskill in this and related arts, for as many items listed.

Having described preferred embodiments of a system and method forfrequency doubling with bipolar transistor frequency doublers atmillimeter-wave frequencies (which are intended to be illustrative andnot limiting), it is noted that modifications and variations can be madeby persons skilled in the art in light of the above teachings. It istherefore to be understood that changes may be made in the particularembodiments disclosed which are within the scope of the invention asoutlined by the appended claims. Having thus described aspects of theinvention, with the details and particularity required by the patentlaws, what is claimed and desired protected by Letters Patent is setforth in the appended claims.

What is claimed is:
 1. A frequency multiplier comprising: a pair oftransistors each connected to a common impedance through a respectivecollector impedance formed from a transmission line, said transmissionline having a length between about one quarter and about one eighth of awavelength of an input signal frequency and being tuned to produce alarge impedance at a collector of the respective transistor at the inputsignal frequency, wherein an output frequency between the collectorimpedances and the common impedance is an even integer multiple of aninput frequency; a pair of reflecting transmission lines having an openend; and a pair of phase shifting transmission lines, each connecting abase terminal of a transistor to a respective one of the pair ofreflecting transmission lines.
 2. The frequency multiplier of claim 1,wherein the length of the transmission line is about one quarter awavelength of an input signal frequency.
 3. The frequency multiplier ofclaim 2, wherein the output frequency is about double the inputfrequency.
 4. The frequency multiplier of claim 1, further comprising apair of neutralization capacitors, each connecting the base terminal ofa transistor to an opposite collector transmission line to compensatefor feedback capacitance in the transistors.
 5. The frequency multiplierof claim 1, wherein the pair of transistors is differentially driven,such that a fundamental component of the input signal cancels out. 6.The frequency multiplier of claim 1, wherein the reflecting transmissionlines have a length that corresponds to about one quarter wavelength ofa frequency-doubled input signal.
 7. The frequency multiplier of claim1, wherein the phase shifting transmission lines have a length thatphase shifts a reflected signal from the reflecting transmission linesto add constructively with harmonic components of the input signal.